Slide 1A Foundation for ProgrammingArraysMany Variables of the Same TypeMany Variables of the Same TypeMany Variables of the Same TypeArrays in JavaArrays in JavaVector Dot ProductArray-Processing ExamplesSlide 11Setting Array Values at Compile TimeSetting Array Values at Run TimeSlide 14War Story (PlanetPoker.com)ShufflingShuffling a Deck of Cards: Putting Everything TogetherCoupon Collector: Scientific ContextCoupon Collector ProblemCoupon Collector: Mathematical ContextCoupon Collector: Java ImplementationSlide 22Two-Dimensional ArraysTwo-Dimensional Arrays in JavaSetting 2D Array Values at Compile TimeMatrix AdditionMatrix MultiplicationArray ChallengeSummaryModule 3: Arrays (Chapter 1.4)Introduction to Programming in Java: An Interdisciplinary Approach · Robert Sedgewick and Kevin Wayne · Copyright © 2002–2010 · 1/14/19 06:26:24 AM2A Foundation for Programmingobjectsfunctions and modulesgraphics, sound, and image I/Oarraysany program you might want to writeconditionals and loopsMath text I/Oassignment statementsprimitive data typesstore and manipulatehuge quantities of data3ArraysStore and manipulate huge quantities of data. Examples.52 playing cards in a deck.All the students in CSE 1311 million characters in a book.10 million audio samples in an MP3 file.Example question: 1) valentine’s chocolate problem2) Output a sorted set of cards3) Output a shuffled set of cards4Many Variables of the Same TypeGoal. 10 variables of the same type.// tedious and error-pronedouble a0, a1, a2, a3, a4, a5, a6, a7, a8, a9; a0 = 0.0;a1 = 0.0;a2 = 0.0;a3 = 0.0;a4 = 0.0;a5 = 0.0;a6 = 0.0;a7 = 0.0;a8 = 0.0;a9 = 0.0;…a4 = 3.0;…a8 = 8.0;…double x = a4 + a8;5Many Variables of the Same TypeGoal. 10 variables of the same type.double[] a; // declarationa = new double[10]; // creation…a[4] = 3.0;…a[8] = 8.0;…double x = a[4] + a[8];6Many Variables of the Same TypeGoal. 1 million variables of the same type.// scales to handle large arraysdouble[] a = new double[1000000];…a[123456] = 3.0;…a[987654] = 8.0;…double x = a[123456] + a[987654];declares, creates, and initializesin a same sentence7Arrays in JavaJava has special language support for arrays.To make an array: declare, create, and initialize it.To access entry i of array named a, use a[i]. Array indices start at 0.Size of an array a: a.lengthint N = 10; // size of arraydouble[] a; // declare the arraya = new double[N]; // create the arrayfor (int i = 0; i < N; i++) // initialize the array a[i] = 0.0; // all to 0.08Arrays in JavaJava has special language support for arrays.To make an array: declare, create, and initialize it.To access entry i of array named a, use a[i]. Array indices start at 0.Compact alternative. Declare, create, and initialize in one statement.Default initialization: all numbers automatically set to zero.int N = 10; // size of arraydouble[] a = new double[N]; // declare, create, initint N = 10; // size of arraydouble[] a; // declare the arraya = new double[N]; // create the arrayfor (int i = 0; i < N; i++) // initialize the array a[i] = 0.0; // all to 0.09Vector Dot ProductDot product. Given two vectors x[] and y[] of length N, their dot product is the sum of the products of their corresponding components.double[] x = { 0.3, 0.6, 0.1 }; double[] y = { 0.5, 0.1, 0.4 }; int N = x.length;double sum = 0.0; for (int i = 0; i < N; i++) { sum = sum + x[i]*y[i];}This syntax initializes an array with the listed values.10Array-Processing ExamplesIf you didn’t know about Double.NEGATIVE_INFINITY, can you think of another way to initialize max?Output a Deck12Setting Array Values at Compile TimeEx. Print a random card.String[] rank = { "2", "3", "4", "5", "6", "7", "8", "9", "10", "Jack", "Queen", "King", "Ace"}; String[] suit = { "Clubs", "Diamonds", "Hearts", "Spades"};int i = (int) (Math.random() * 13); // between 0 and 12int j = (int) (Math.random() * 4); // between 0 and 3System.out.println(rank[i] + " of " + suit[j]);Safer, and easier, to say: rank.length instead of 1313Setting Array Values at Run TimeEx. Create a deck of playing cards and print them out.Q. In what order does it output them?A. B.String[] deck = new String[52];for (int i = 0; i < 13; i++) for (int j = 0; j < 4; j++) deck[4*i + j] = rank[i] + " of " + suit[j];for (int k = 0; k < 52; k++) System.out.println(deck[k]);typical array-processing code changes valuesat runtimetwo of clubstwo of diamondstwo of heartstwo of spadesthree of clubs...two of clubsthree of clubsfour of clubsfive of clubssix of clubs...Shuffling a Deck15War Story (PlanetPoker.com)Texas hold 'em poker. Software must shuffle electronic deck of cards.How we learned to cheat at online poker: a study in software securityhttp://itmanagement.earthweb.com/entdev/article.php/61622116ShufflingGoal. Given an array, rearrange its elements in random order.Shuffling algorithm.In iteration i, pick random card from deck[i] through deck[N-1], with each card equally likely.Exchange it with deck[i].int N = deck.length;for (int i = 0; i < N; i++) { int r = i + (int) (Math.random() * (N-i)); String t = deck[r]; deck[r] = deck[i]; deck[i] = t;}between i and N-1swapidiom17Shuffling a Deck of Cards: Putting Everything Togetherpublic class Deck { public static void main(String[] args) { String[] suit = { "Clubs", "Diamonds", "Hearts", "Spades" }; String[] rank = { "2", "3", "4", "5", "6", "7", "8", "9", "10", "Jack", "Queen", "King", "Ace" }; int SUITS = suit.length; int RANKS = rank.length; int N = SUITS * RANKS; String[] deck = new String[N]; for (int i = 0; i < RANKS; i++) for (int j = 0; j < SUITS; j++) deck[SUITS*i + j] = rank[i] + " of " + suit[j]; for (int i = 0; i < N; i++) { int r = i + (int) (Math.random() * (N-i)); String t = deck[r]; deck[r] = deck[i]; deck[i] = t; } for (int i = 0; i < N; i++) System.out.println(deck[i]); }}avoid "hardwired" constantsbuild the deckshuffleprint shuffled deck18Coupon Collector: Scientific ContextQ. Given a sequence from nature, does it have same characteristicsas a random sequence?A. No easy answer - many tests have been developed.Coupon collector test. Compare number of elements that need to be examined before all values are found against the